Monday, September 13, 2010

What fraction of this year’s graduating students at a certain college are males?

(1) Of this year’s graduating students, 33 percent of the males and 20 percent of the females transferred from another college.
(2) Of this year’s graduating students, 25 percent transferred from another college.




hopefully it's fairly clear, after a little reflection, that each of the individual statements is insufficient; they're merely statements about percentages / proportions of students who transferred from other colleges. that won't do to figure out percentages of the entire graduating class.
BUT:
let's say M is the # of males in the graduating class (total), and F is the # of females.
then
statement (1) says 0.33M + 0.20F were transfers;
statement (2) says 0.25(M + F) were transfers (i.e., 25% of everybody).

since both of these are the # of transfers, set them equal:
0.33M + 0.20F = 0.25M + 0.25F
0.08M = 0.05F
this gives you the ratio of males to females if you continue to solve (which, of course, you don't have to)

...but, if you have the ratio of m : f (and there's no third gender, hopefully) that's SUFFICIENT to find the percentages.

Hint - One can do double matrix and find the solution by using 'C'...similar to Weighted average problem....

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